1. Field of the Invention
The present invention relates to signal delay circuits, FIR (finite impulse response) filters, and musical tone synthesizing devices which employ signal delay circuits and/or FIR filters.
2. Prior Art
Methods of synthesizing the musical sounds of conventional musical instruments (non-electronic) are known in which the mechanism of sound generation in the musical instrument is simulated to obtain a tone generation model which is then applied to the synthesis of the sounds of the target musical instrument. In Japan, such methods have been disclosed in, for example, Japanese Patent Application Laid-Open, No. 63-40199, and U.S. Pat. No. 4,130,043. Below, a conventional musical tone synthesizing device based on this technology will be described.
In FIG. 1, the layout of a musical tone synthesizer is schematically shown in which the musical tone generation of a woodwind instrument is simulated. In the drawing, ROM (read only memory) 11 is shown in which a data table for a non-linear function expressing the response characteristics of the reed of a woodwind instrument are recorded.
Loop circuit 12 simulates the tubular portions of the woodwind instrument, that is, loop circuit 12 simulates the resonator tube transmission characteristics of the instrument. In loop circuit 12, multiple delay circuits having a fixed delay are arranged in series. Additionally, connected into the loop circuit 12 at their respective corresponding locations are various elements including junction units (impedance coupling circuits) for simulating the dispersion of generated air pressure waves created at locations in the tubular portions where the diameter varies and at tone holes. Additionally, filters, etc. are provided at corresponding locations which simulate acoustic losses occurring within each part of the resonator tube. In general, to the extent that the frequency of the generated sound is high, acoustic losses are great. For this reason, low pass filters are used for the above mentioned filters included in the loop circuit 12.
Pressure data PD corresponding to the air pressure applied at the reed by a performer playing an actual woodwind instrument is supplied to subtracter circuit 13, and from this supplied data value, the feedback signal (this value corresponds to the pressure of the reflected pressure wave from the resonator tube) from loop circuit 12 is subtracted, the result of the subtraction operation then supplied to ROM 11.
With a circuit so constructed, pressure data PD corresponding to the air pressure applied to a reed is supplied as address data to ROM 11 via subtracter circuit 13. After the address data is supplied to ROM 11 from subtracter circuit 13, data corresponding to the address data is output from ROM 11 which then travels through loop circuit 12, then returning to subtracter circuit 13. The returned value is then subtracted from the pressure data PD which is currently being supplied to subtracter circuit 13, the result of the subtraction again supplied to ROM 11, and the cycle is then repeated. Thus, it can be seen from this discussion and from FIG. 1 that a closed loop is established by this construction. Accordingly, data is caused to propagate within a closed loop in which a resonance function is established, whereby a musical signal is output.
With this kind of musical tone synthesizer, to the extent that the supplied pressure data PD corresponds to a high air pressure, the fidelity improves for the generated frequency spectrum of the simulated reed vibration, as well as for the musical effect of simulated transmission characteristics of air pressure waves from tubular portions of the instrument. Thus, to the extent that the supplied pressure data PD corresponds to a high value, a more natural sound is synthesized, that is, a sound that more closely corresponds to the sound of the actual musical instrument being simulated.
Simulation of the musical sound of string instruments can be achieved using a circuit similar that shown in FIG. 1. In such a case, ROM 11 holds a data table for a non-linear function expressing the elastic characteristics of the strings of the string instrument. When simulating a string instrument, loop circuit 12 simulates the propagation characteristics of vibrations in the strings of the string instrument. Just as with simulation of a woodwind instrument, loop circuit 12 includes multiple delay circuits having a fixed delay which are arranged in series. Similar to the simulation of a woodwind instrument, loop circuit 12 includes filters, junction units, etc. at their corresponding locations for simulating the resonator box, acoustic losses and other characteristics of the string instrument.
For simulation of the sound of either a woodwind instrument or a string instrument, by adjusting the delay interval of the signal propagated in the loop circuit 12, the resonant frequency can be adjusted, that is, the pitch of the generated sound can be adjusted. Basically, in this type of circuit, the delay interval of the signal propagated in the loop circuit 12 is adjusted by a switch means whereby the number of individual delay circuits in series with the loop can be selected.
However, with the pitch control as described in the preceding paragraph, the loop circuit 12 delay interval must necessarily be an integral multiple of the delay interval of one individual delay circuit. Accordingly, only pitches of which the fundamental frequency is given by: EQU f=1/n.tau. where n=1, 2, 3, . . . .
can be generated. Thus, considerable limitations exist in regard to the pitches that can be generated with this kind of circuit. In addition to not being able to freely select a pitch to be generated, because the range of pitches that can be generated is noncontinuous, it is not possible to incorporate "pitch benders", vibrato functions, and other control means that rely on variation of pitch over a continuous range.
In FIG. 2, a circuit diagram for a musical tone synthesizer is shown suitable for generation of musical tones in which the envelope of a piano or similar instrument is simulated, wherein the maximum sound intensity occurs immediately after the tone is initiated, followed by a gradual decrease in intensity. Compared with a percussion instrument such as a drum the envelope of which also demonstrates maximum sound intensity immediately following the onset of the sound, the decline in sound intensity is relatively prolonged with a piano. In the case of a horn or woodwind instrument, both the timing of maximum intensity and the decline in intensity are delayed compared with a piano or drum.
As shown in the diagram, an adder circuit 1, delay circuit 2, FIR (finite impulse response) filter 3, and multiplier circuit 4 are sequentially provided, thereby forming a closed loop. In the illustrated circuit, the delay circuit 2 consists of a plurality of delay elements serially provided, whereby the input signal is delayed by a sampling time .tau..sub.s, and then output to FIR filter 3. Based on pitch data supplied to the delay circuit 2 from a pitch control circuit (not shown in the drawing), the number of delay stages n and hence the sampling time .tau..sub.s can be selected. The multiplier coefficient g for multiplier circuit 4 is selected so that the value for the closed loop gain from adder circuit 1 to delay circuit 2 to FIR filter 3 to multiplier circuit 4 back to adder circuit 1 again is slightly smaller than 1.
As shown in FIG. 2, FIR filter 3 is made up of delay circuit 5 wherein the input signal to FIR filter 3 is delayed by a sampling time .tau..sub.s and then output, multiplier circuit 6 wherein the FIR filter 3 input signal is multiplied by 1-.alpha. and then output, multiplier circuit 7 to which the output of delay circuit 5 is supplied where it is multiplied by .alpha. and then output, and adder circuit 8 wherein the output of multiplier circuit 6 and multiplier circuit 7 are added and then output. This FIR filter 3 functions as a timbre control low pass filter, wherein the coefficient .alpha. is chosen so as be between 0 and 0.5.
Below, the characteristics of FIR filter 3 will be described. For an FIR filter circuit having the layout shown in FIG. 2, the impulse response function H.sub.1 (z) is expressed by Equ. 1 shown below. EQU H.sub.1 (z)=1-.alpha.+.alpha.z.sup.-1 Equ. 1
The frequency characteristics f.sub.1 (.omega.) of the FIR filter circuit, where .omega. indicates the angular frequency of the input signal, are given by substituting exp(-j.omega..tau..sub.s) for z.sup.-1 in Equ. 1 resulting in Equ. 2 shown below. ##EQU1## The amplitude A.sub.1 (.omega.) is then given by Equ. 3 below. ##EQU2## According to Equ. 3, to the extent that angular frequency .omega. is large, A.sub.1 (.omega.) becomes small. Here .omega. is defined so as to satisfy the relation .omega..tau..sub.s .ltoreq..pi./2. Thus, it can be seen that the FIR filter 3 functions as a low pass filter.
The phase characteristics P.sub.1 (.omega.) are given by Equ. 4 below. ##EQU3## In Equ. 4, arctan(F.sub.1 (.omega.)) expresses the phase angle of F.sub.1 (.omega.). In the musical tone synthesizer circuit under discussion, the angular frequency .omega. of the input signal is significantly small compared with sampling frequency f.sub.s which equals 1/.tau..sub.s. Accordingly, assuming the approximation tan.sup.-1 x.congruent.x which is true for sufficiently small values of x, and further assuming that cos.omega..tau..sub.s .congruent.1 and that sin.omega..tau..sub.s .congruent..omega..tau..sub.s which are true given that .omega. is sufficiently small, the approximate equivalence shown in Equ. 5 below can be derived from Equ. 4. EQU P.sub.1 (.omega.).congruent.-.alpha..omega..tau..sub.s Equ. 5
Accordingly, the effective delay interval .tau..sub.a of the FIR filter 3 is given by Equ. 6 below. ##EQU4##
With the musical tone synthesizer circuit under discussion, under ordinary circumstances, a signal having a great number of frequency components, for example an impulse signal, is supplied to adder circuit 1. From adder circuit 1, the signal is successively supplied to delay circuit 2, FIR filter 3, multiplier circuit 4, and then back again to adder circuit 1 to repeat the cycle, traveling over the closed loop thus formed.
For a delay circuit 2 delay interval of n.tau..sub.s and a delay interval of .tau..sub.a for the FIR filter 3 as a whole, the required time .tau. for a signal to traverse one complete lap of the musical tone synthesizer circuit shown in FIG. 2 is given by Equ. 7 below. EQU .tau.=n.tau..sub.s +.tau..sub.a Equ. 7
In this case, the closed loop gain frequency characteristics of the circuit are such that, the frequency spectrum for the generated signal exhibits maximum values at integral multiples of the fundamental frequency f.sub.1 which equals 1/.tau.. Accordingly, among the frequency components of an input impulse signal, only those frequencies equal to the above mentioned fundamental frequency f.sub.1 and harmonics which are integral multiples thereof continue to circulate around the closed loop circuit, other frequency components being effectively suppressed. For the frequency components that continue to circulate around the closed loop circuit, each component is governed according to the amplitude characteristics given by Equ. 3 above. In this way, the wave form of the signal the propagates over the closed loop circuit, that is the timbre of the musical signal, is regulated. Due to the fact, as stated above, that the multiplier coefficient g for multiplier circuit 4 is selected so that the value for the closed loop gain is slightly smaller than 1, the amplitude of the circulating signal gradually diminishes. In the closed loop circuit under discussion, the output of adder circuit 1 is used as the musical output signal.
With the above described FIR filter 3, as can be understood from Equ. 6 above, when coefficient .alpha. is varied, the delay interval .tau..sub.a in turn varies. Thus, with this kind of conventional musical tone synthesizer circuit employing an FIR filter for timbre control as part of a closed loop circuit, when an attempt is made to adjust the timbre by varying multiplier coefficient .alpha., and hence 1-.alpha., because the delay interval for the closed loop circuit as a whole varies, the pitch of the generated tone ends up varying as well which is undesirable.